CN105353269A - On-line fault distance measurement method for high-voltage cable - Google Patents

Abstract

The invention relates to an on-line fault distance measurement method for a high-voltage cable, and the method comprises the steps: (1) collecting transient traveling wave current signals at the head and tail ends of a cable; (2) enabling the current signals obtained at step (1) to be converted into independent analog current signals i1-i6 through phase-mode transformation; (3) selecting the analog current signal i4 at step (2) for wavelet packet decomposition, solving an energy ratio of all frequency bands through employing a wavelet packet decomposition coefficient, then extracting the frequency band with the high energy ratio, and reconfiguring a transient traveling wave; (4) carrying out the wavelet analysis of the configured transient traveling wave at step (3), and determining the time t1 and T1 when the configured transient traveling wave arrives at the head and tail ends of the cable; (5) judging a fault region according to the time t1 and T1 at step (4), and solving a geographic distance from a fault point to the head end of the cable. Compared with the prior art, the method is high in distance measurement precision, and is few in interference.

Description

The online fault distance-finding method of a kind of high-tension cable

Technical field

The present invention relates to a kind of cable fault localization method, especially relate to the online fault distance-finding method of a kind of high-tension cable.

Background technology

Power cable is generally embedded in underground, and fault is accurately located and repaired more difficult, and fault occurs in cable line can cause great economic loss usually.Study cable fault localization method fast, accurately to contribute to reducing the fault line walking time, repair fault as early as possible, reduce because of the economic loss caused that has a power failure, to ensureing that the power supply reliability of urban distribution network has very important significance.

Cable fault localization method is divided into off-line distance-finding method and online distance-finding method usually, and online distance-finding method is also immature, and what generally adopt at present is the fault locator of offline mode.Because high-tension cable charging current is larger and fault mostly is high resistant or flashover fault, be difficult to produce sufficiently high voltage in reality trouble spot is punctured, and the earthing mode that high-tension cable generally adopts metal sheath layer cross interconnected, row wave traveling is to cross interconnected point and direct earth point, can be discontinuous because of wave impedance, thus cause the propagation on cross interconnected cable of row ripple can produce complicated catadioptric, cause trouble spot reflection wave to be difficult to identify.At direct earth point, outer modulus can be grounded an interception and flow into the earth, and interior modulus is then passed through intactly, and namely at direct earth point, outer modulus traveling-waves disturbs to interior modulus row wavestrip.At cross interconnected point, can there is mutual conversion because of the catadioptric of row ripple in inside and outside modulus, and because inside and outside modulus velocity of wave is different, the overall velocity of wave of row ripple shows as the mixing velocity of wave of inside and outside modulus.For direct-buried cable, interior modulus velocity of wave is greater than outer modulus velocity of wave, and interior modulus traveling-waves first arrives measurement point, and outer modulus can not disturb interior modulus traveling-waves.Lay or cable that tunnel lays for built on stilts, outer modulus traveling wave speed is greater than interior modulus velocity of wave, and outer modulus traveling-waves first arrives measurement point, bring interference can to the identification of interior modulus wavefront, causes interior modulus wavefront to be difficult to identify.

Therefore, the fault localization of offline mode is not suitable for the fault localization of high-tension cable, is only applicable to the fault localization of electric pressure at the mesolow cable of below 35KV.

Fault localization for cross interconnected cable needs first to determine faulty section, unties cross interconnected point, and just can carry out fault localization, expend time in length, and workload is large.Along with the widespread use of high voltage electric transmission cable, the online Fault Location Algorithm that research is applicable to high-tension cable is necessary.The transient state travelling wave produced during cable fault has continuous frequency spectrum from low to high, and because the row velocity of wave propagation of different frequency component is different, decay is also different, and row ripple dispersion can occur along in cable line communication process.Wavefront is tended towards stability, and overall velocity of wave is tending towards declining, and brings very large difficulty to the determination of the identification of wave head in travelling wave ranging and velocity of wave.For the fault localization of overhead transmission line, Yan Shangke accepts the error produced by row wave dispersion, and stronger for frequency dependent characteristic, and distance accuracy requires that higher cable line is but unacceptable.The online location algorithm of traditional high-tension cable generally all supposes that row ripple velocity of propagation is in the cable constant, and do not consider that the change of cable operational factor and row wave dispersion are on the impact of traveling wave speed, distance accuracy is not high.

Summary of the invention

Object of the present invention be exactly provide that a kind of distance accuracy is high to overcome defect that above-mentioned prior art exists, convenience of calculation, the online fault distance-finding method of high-tension cable that interference is few.

Object of the present invention can be achieved through the following technical solutions: the online fault distance-finding method of a kind of high-tension cable, comprises the following steps:

(1) signals collecting: gather transient state travelling wave current signal at cable end at the whole story;

(2) phase-model transformation: convert the current signal in step (1) to 6 mutual independently modulus current signal i by phase-model transformation ₁~ i ₆;

(3) decomposition and reconstruction of transient state travelling wave: the modulus current signal i in selecting step (2) ₄carry out WAVELET PACKET DECOMPOSITION, utilize WAVELET PACKET DECOMPOSITION coefficient to try to achieve the energy Ratios of each frequency band, then extract the frequency band of energy percentage >5%, reconstruct transient state travelling wave; By the decomposition and reconstruction to transient state travelling wave, effectively reduce the frequency span of transient state travelling wave, reduce the impact of transient state travelling wave dispersion on range measurement.

(4) wavelet analysis: carry out wavelet analysis to the transient state travelling wave after reconstruct in step (3), determines that the capable ripple of initial transient arrives the time t of cable head-end ₁with the time T arriving cable end piece ₁;

(5) trouble spot calculates apart from the geographic distance of cable head-end: according to t in step (4) ₁, T ₁the region that occurs of size failure judgement, if fault occurs in cable first half section, then obtain the time T that cable end piece second transient state travelling wave wave head arrives measurement point ₂, and then obtain fault distance; If fault occurs in the cable second half section, then obtain the time t that cable head-end second transient state travelling wave wave head arrives measurement point ₂, and then obtain the geographic distance of trouble spot apart from cable head-end.

Modulus current signal i in described step (2) ₁~ i ₆calculating formula as follows:

$\left\{\begin{array}{c}{i}_1=\frac{1}{\sqrt{3}}(i_a+i_b+i_c+i_A+i_B+i_C)\\ i_2=\frac{1}{\sqrt{6}}(i_a-2i_b+i_c+i_A-2i_B+i_C)\\ i_3=\frac{1}{\sqrt{2}}(i_a-i_c+i_A-i_C)\end{array}\right.\left\{\begin{array}{c}{i}_4=-\frac{1}{\sqrt{3}}(i_a+i_b+i_c)\\ i_5=-\frac{1}{\sqrt{6}}(i_a-2i_b+i_c)\\ i_6=-\frac{1}{\sqrt{2}}(i_a-i_c)\end{array}\right.$

Wherein, i _a, i _b, i _cbe respectively a phase core electric current, b phase core electric current, c phase core electric current, i _a, i _b, i _cbe respectively a phase sheath electric current, b phase sheath electric current, c phase sheath electric current.

Described step (3) is specially:

(301) adopt wavelet packet analysis method by modulus current signal i ₄be decomposed into low-frequency approximation part and high frequency detail part, more described low-frequency approximation part is become second layer low frequency part and HFS with high frequency detail decomposed, decompose through i layer, modulus current signal i ₄. be just decomposed 2 ⁱindividual different frequency band, utilizes the size of each frequency band energy of WAVELET PACKET DECOMPOSITION coefficient calculations, and the energy meter formula of each frequency band is as follows:

$E_{i,j}=\underset{k=1}{\overset{N}{\Σ}}{\left|d_{j,k}\right|}^2$

Wherein, i is the number of plies of WAVELET PACKET DECOMPOSITION, and N is the sampling number of travelling wave signal.D _j,k(j=0,1,2 ... 2 ⁱ-1, k=1,2 ... N) the WAVELET PACKET DECOMPOSITION coefficient of expression i-th layer, a jth node;

For cross interconnected cable, select modulus current signal i ₄as travelling wave ranging signal, the interference problem that the transmission of inside and outside modulus intersection brings to travelling wave ranging can be eliminated to greatest extent.

(302) energy of i-th layer of each frequency band is normalized, the number percent η shared by each frequency band energy can be obtained _j, its calculating formula is as follows:

${\mathrm{\η}}_j=\frac{E_{i,j}}{\underset{j=0}{\overset{2^i-1}{\Σ}}{E}_{i,j}}\×100\%$

(303) η is extracted _jthe frequency band of >5%, reconstruct fault transient travelling wave.The frequency band being greater than 5% by extracting energy percentage in fault transient travelling wave carries out the reconstruct of transient state travelling wave, the frequency band that energy percentage is lower, very little on range measurement impact can be removed like this, effectively reduce the frequency span of transient state travelling wave, reduce the impact of row wave dispersion on range measurement, improve fault localization precision;

Described step (5) is specially: if t ₁<T ₁, then illustrate that fault occurs in cable first half section, obtain the time T that cable end piece second transient state travelling wave wave head arrives measurement point ₂, obtain the geographic distance L of trouble spot apart from cable head-end further _f, L _fcalculating formula is as follows:

$L_f=\frac{L(T_2-T_1)}{2(T_2-t_1)},$

Wherein, L is the geographical length of cable;

If t ₁>T ₁, then illustrate that fault occurs in the cable second half section, obtain the time t that cable head-end second transient state travelling wave wave head arrives measurement point ₂, obtain the geographic distance L of trouble spot apart from cable head-end further _f, L _fcalculating formula is as follows:

$L_f=L-\frac{L(t_2-t_1)}{2(t_2-T_1)},$

Wherein, L is the geographical length of cable.

Described trouble spot is apart from the distance L of cable head-end _fcalculating formula derivation as follows: in reality, cable generally adopts snake laying, the physical length of cable and geographical length are also unequal, if the physical length of cable is l, geographical length is L, suppose that relation is between the two approximately: l=λ L, λ is the scale-up factor between cable physical length l and geographical length L

1., when fault occurs in cable first half section, transient state travelling wave velocity of wave is in the cable:

$\left\{\begin{array}{c}v=\frac{l}{T_2-t_1}\\ l=\mathrm{\&lambda;}L\end{array}\right.---\left(1\right)$

Trouble spot apart from the actual range of cable head-end is:

$\left\{\begin{array}{c}{l}_f=\frac{1}{2}v(T_2-T_1)\\ l_f=\mathrm{\&lambda;}{L}_f\end{array}\right.---\left(2\right)$

The geographic distance L of trouble spot apart from cable head-end is tried to achieve according to formula (1) and formula (2) _ffor:

$L_f=\frac{L(T_2-T)}{2(T_2-t_1)};$

2., when fault occurs in the cable second half section, transient state travelling wave velocity of wave is in the cable:

$\left\{\begin{array}{c}v=\frac{l}{t_2-T_1}\\ l=\mathrm{\&lambda;}L\end{array}\right.---\left(3\right)$

Trouble spot apart from the actual range of cable head-end is:

$\left\{\begin{array}{c}{l}_f=l-\frac{1}{2}v(t_2-t_1)\\ l_f=\mathrm{\&lambda;}{L}_f\end{array}\right.---\left(4\right)$

The geographic distance L of trouble spot apart from cable head-end is tried to achieve according to formula (3) and formula (4) _ffor:

$L_f=L-\frac{L(t_2-t_1)}{2(t_2-T_1)}.$

These computing method are not by the online Algorithms of Travelling Wave Based Fault Location of impact of cable velocity of wave change, and algorithm take into account the snake laying of cable, adopts this algorithm known conditions carried out needed for transient state travelling wave range finding to be only the geographical length of cable, convenience of calculation;

The calculating of 1 cable modulus current signal

Six conductor systems that three-phase single-core power cables is made up of conductor wire core and protective metal shell, coupling is there is between this six conductor system, find range to adopt transient state travelling wave method in cable system, must independently modulus signal be become mutually to analyze by phase-model transformation matrix conversion the voltage of cable, current signal, adopt expansion Clark matrix to carry out phase-model transformation to cable system.Because outer modulus is with metal sheath layer with greatly for loop, propagation characteristic is unstable, and attenuation coefficient is large, and therefore we mainly study the transport property of modulus electric current in cable.Modulus current signal i ₁~ i ₆the calculating formula under expansion Clark matrixing as follows:

Wherein, i _a, i _b, i _cbe respectively a phase core electric current, b phase core electric current, c phase core electric current, i _a, i _b, i _cbe respectively a phase sheath electric current, b phase sheath electric current, c phase sheath electric current, i ₁, i ₂, i ₃for outer modulus current signal, i ₄, i ₅, i ₆for interior modulus current signal.

The solution that in 2, modulus and outer modulus velocity of wave disturb

For cross interconnected cable, because the coordinated transposition of metal sheath layer connects, before and after POI, wave impedance is discontinuous.To the wave impedance matrix Z before POI ₁row, column carry out corresponding transposition can obtain POI after wave impedance matrix Z ₂, i.e. Z ₂=PZ ₁p ^t.For the transposition situation shown in Fig. 3, conversion bit matrix P is:

$P=\left[\begin{array}{cccccc}1& & & & & \\ & 1& & & & \\ & & 1& & & \\ & & & & & 1\\ & & & 1& & \\ & & & & 1& \end{array}\right]$

Wherein the putting in order as a phase core, b phase core, c phase core, a phase protective metal shell, b phase protective metal shell, c phase protective metal shell of impedance matrix.

By can be calculated the cable that certain 220kv tunnel lays, adopt the cross interconnected mode of Fig. 3, the wave impedance matrix when frequency is 1KHz is:

$Z_1=\left[\begin{array}{cccccc}39.84& 8.12& 6.71& 22.8& 8.13& 6.71\\ 8.12& 39.38& 8.12& 8.13& 22.33& 8.13\\ 6.71& 8.12& 39.84& 6.71& 8.13& 22.8\\ 22.8& 8.13& 6.71& 22.77& 8.14& 6.72\\ 8.13& 22.33& 8.13& 8.14& 22.3& 8.14\\ 6.71& 8.13& 22.8& 6.72& 8.14& 22.7\end{array}\right]$

Wave impedance matrix Z after POI ₂=PZ ₁p ^t, according to Z ₁, Z ₂the refraction coefficient matrix α of the capable ripple of current temporary state can be obtained _iwith reflection coefficient matrix β _i.The catadioptric relation of the capable ripple of current temporary state in modulus territory meets:

$\left\{\begin{array}{c}{i}_q=T_i{I}_{qm}\\ i_0=T_i{I}_{om}\\ i_q={\mathrm{\&alpha;}}_i{i}_0\end{array}\right.$

Wherein: I _omand I _qmbe respectively the incident modulus current matrix and refraction modulus current matrix that are made up of 6 modulus electric currents.Can be obtained fom the above equation: $i_{qm}=T_i^{-1}{\mathrm{\&alpha;}}_i{T}_i\&CenterDot;i_{om}.$

So the capable ripple of current temporary state at the refraction coefficient matrix in modulus territory is: be can be calculated by MATLAB:

${\mathrm{\&alpha;}}_{im}=\left[\begin{array}{cccccc}1.0001& -0.0560& -0.0302& 0.0001& -0.0564& -0.0457\\ -0.0092& 1.8107& 0.7298& -0.0117& 0.4234& 1.1992\\ -0.0059& -0.7132& 1.8949& -0.0055& -1.1612& 0.4894\\ -0.0000& 0.0270& 0.0156& 0.9999& 0.0271& 0.0232\\ 0.0012& -0.8385& -0.4833& 0.0020& 0.1614& -0.7183\\ 0.0040& 0.5015& -0.8670& 0.0045& 0.7262& 0.1332\end{array}\right]$

Pass before and after cross interconnected between modulus electric current is:

[I _qm1i _qm2i _qm3i _qm4i _qm5i _qm6] ^t=α _im[I _om1i _om2i _om3i _om4i _om5i _om6] ^t, α except diagonal entry _imthe element of the 4th row is very little, and is significantly less than other element respectively arranged, and illustrates that the component that modulus current signal 4 is transmitted in other modulus at cross interconnected point is minimum.By α _im44=0.9999, I _qm4=α _im44i _om4known incident modulus current signal 4 substantially all changes into refraction modulus current signal 4 at cross interconnected point, does not reflect.Therefore, adopt modulus current signal 4 as cross interconnected cable transient state travelling wave distance measuring signal, effectively can solve the complicated trouble spot reflection wave caused of transient state travelling wave catadioptric and be difficult to identification problem.

3 transient state travelling wave dispersions are on the impact of fault localization

Core and the metal sheath layer of high-tension cable have skin effect when being connected with alternating current, and the resistance of circuit and inductance can change with the change of power frequency.Circuit can present different transport propertys for the row ripple of different frequency component, and cable system at the propagation coefficient of frequency domain is:

$\mathrm{\&gamma;}\left(\mathrm{\&omega;}\right)=\sqrt{ZY}=\mathrm{\&alpha;}\left(\mathrm{\&omega;}\right)+j\mathrm{\&beta;}\left(\mathrm{\&omega;}\right)$

Wherein: [Z], [Y] are respectively impedance matrix and the admittance matrix of cable, α (ω) is amplitude attenuation coefficient, makes the amplitude attenuation of different frequency signals different; β (ω) is phase coefficient, and make the velocity of wave decay of different frequency signals different, the capable ripple of current temporary state and the capable ripple of voltage transient have identical propagation coefficient.

The transient state travelling wave produced during cable fault has continuous frequency spectrum from low to high, and because the transient state travelling wave velocity of propagation of different frequency component is different, decay is also different, and transient state travelling wave dispersion can occur along in cable line communication process.Transient state travelling wave wave head is tended towards stability, and overall velocity of wave is tending towards declining, and brings very large difficulty to the identification of wave head and the determination of velocity of wave in transient state travelling wave range finding.For the fault localization of overhead transmission line, Yan Shangke accepts the error produced by transient state travelling wave dispersion, and stronger for frequency dependent characteristic, and distance accuracy requires that higher cable line is but unacceptable.

For this reason, the application adopts the wavelet packet method as described in step (3) decompose and reconstruct transient state travelling wave,

4 by the location algorithm that transient state travelling wave velocity of wave affects

The application adopts the location algorithm as described in step (5), wherein, consider that in reality, cable generally adopts snake laying, the physical length of cable is also not easily tried to achieve, if the relation between the physical length l of cable and geographical length L is approximately: l=λ L, λ are the scale-up factor between snake laying cable physical length and geographical length.

Compared with prior art, the present invention has the following advantages:

(1) the application is by the propagation characteristic of research modulus current signal in the cross interconnected cable of high pressure, propose the travelling wave ranging signal using modulus electric current as high-tension cable, efficiently solve the row setback reflection challenge that cross interconnected cablebreak impedance discontinuity causes, and the intersection Transmission Problem of inside and outside modulus traveling-waves;

(2) the application devises not by the online Algorithms of Travelling Wave Based Fault Location of impact of cable velocity of wave change, and algorithm take into account the snake laying of cable, adopts this algorithm known conditions carried out needed for travelling wave ranging to be only the geographical length of cable, convenience of calculation;

(3) the application carries out the reconstruct of transient state travelling wave by the frequency band that energy percentage in extraction fault transient travelling wave is higher, effectively reduces the frequency span of transient state travelling wave, reduces the impact of row wave dispersion on range measurement, improve fault localization precision;

(4) for cross interconnected cable, modulus current signal i is selected ₄as travelling wave ranging signal, the interference problem that the transmission of inside and outside modulus intersection brings to travelling wave ranging can be eliminated to greatest extent.

Accompanying drawing explanation

The online fault distance-finding method process flow diagram of Fig. 1 high-tension cable;

The single-core crosslinked Polyethylene insulated cable structural drawing of Fig. 2;

The transition diagram of the inside and outside modulus of the cross interconnected cable of Fig. 3;

Fig. 4 wavelet decomposition tree schematic diagram;

The catadioptric schematic diagram of transient state travelling wave during the first half segment fault of Fig. 5 cable;

The catadioptric schematic diagram of transient state travelling wave during Fig. 6 cable second half section fault;

Transient state travelling wave during Fig. 7 cable fault;

Fig. 8 top transient state travelling wave frequency band energy number percent;

Fig. 9 end transient state travelling wave frequency band energy number percent;

Transient state travelling wave after Figure 10 reconstruct;

Figure 11 cable system realistic model.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

As shown in Figure 1, the online fault distance-finding method of a kind of high-tension cable, comprises the following steps:

(1) signals collecting: gather transient state travelling wave current signal at cable end at the whole story;

(2) phase-model transformation: convert the current signal in step (1) to 6 mutual independently modulus current signal i by phase-model transformation ₁~ i ₆;

(3) decomposition and reconstruction of transient state travelling wave: the modulus current signal i in selecting step (2) ₄carry out WAVELET PACKET DECOMPOSITION, utilize WAVELET PACKET DECOMPOSITION coefficient to try to achieve the energy Ratios of each frequency band, then extract the frequency band of energy percentage >5%, reconstruct transient state travelling wave; By the decomposition and reconstruction to transient state travelling wave, effectively reduce the frequency span of transient state travelling wave, reduce the impact of transient state travelling wave dispersion on range measurement.

(4) wavelet analysis: carry out wavelet analysis to the transient state travelling wave after reconstruct in step (3), determines that the capable ripple of initial transient arrives the time t of cable head-end ₁with the time T arriving cable end piece ₁;

(5) trouble spot calculates apart from the geographic distance of cable head-end: according to t in step (4) ₁, T ₁the region that occurs of size failure judgement, if fault occurs in cable first half section, then obtain the time T that cable end piece second transient state travelling wave wave head arrives measurement point ₂, and then obtain fault distance; If fault occurs in the cable second half section, then obtain the time t that cable head-end second transient state travelling wave wave head arrives measurement point ₂, and then obtain the geographic distance of trouble spot apart from cable head-end.

Modulus current signal i in described step (2) ₁~ i ₆calculating formula as follows:

$\left\{\begin{array}{c}{i}_1=\frac{1}{\sqrt{3}}(i_a+i_b+i_c+i_A+i_B+i_C)\\ i_2=\frac{1}{\sqrt{6}}(i_a-2i_b+i_c+i_A-2i_B+i_C)\\ i_3=\frac{1}{\sqrt{2}}(i_a-i_c+i_A-i_C)\end{array}\right.\left\{\begin{array}{c}{i}_4=-\frac{1}{\sqrt{3}}(i_a+i_b+i_c)\\ i_5=-\frac{1}{\sqrt{6}}(i_a-2i_b+i_c)\\ i_6=-\frac{1}{\sqrt{2}}(i_a-i_c)\end{array}\right.$

Wherein, i _a, i _b, i _cbe respectively a phase core electric current, b phase core electric current, c phase core electric current, i _a, i _b, i _cbe respectively a phase sheath electric current, b phase sheath electric current, c phase sheath electric current.

Described step (3) is specially:

(301) adopt wavelet packet analysis method by modulus current signal i ₄be decomposed into low-frequency approximation part and high frequency detail part, more described low-frequency approximation part is become second layer low frequency part and HFS with high frequency detail decomposed, decompose through i layer, modulus current signal i ₄. be just decomposed 2 ⁱindividual different frequency band, utilizes the size of each frequency band energy of WAVELET PACKET DECOMPOSITION coefficient calculations, and the energy meter formula of each frequency band is as follows:

$E_{i,j}=\underset{k=1}{\overset{N}{\&Sigma;}}{\left|d_{j,k}\right|}^2$

Wherein, i is the number of plies of WAVELET PACKET DECOMPOSITION, and N is the sampling number of travelling wave signal.D _j,k(j=0,1,2 ... 2 ⁱ-1, k=1,2 ... N) the WAVELET PACKET DECOMPOSITION coefficient of expression i-th layer, a jth node;

For cross interconnected cable, select modulus current signal i ₄as travelling wave ranging signal, the interference problem that the transmission of inside and outside modulus intersection brings to travelling wave ranging can be eliminated to greatest extent.

(302) energy of i-th layer of each frequency band is normalized, the number percent η shared by each frequency band energy can be obtained _j, its calculating formula is as follows:

${\mathrm{\&eta;}}_j=\frac{E_{i,j}}{\underset{j=0}{\overset{2^i-1}{\&Sigma;}}{E}_{i,j}}\&times;100\%$

(303) η is extracted _jthe frequency band of >5%, reconstruct fault transient travelling wave.The frequency band being greater than 5% by extracting energy percentage in fault transient travelling wave carries out the reconstruct of transient state travelling wave, the frequency band that energy percentage is lower, very little on range measurement impact can be removed like this, effectively reduce the frequency span of transient state travelling wave, reduce the impact of row wave dispersion on range measurement, improve fault localization precision;

Described step (5) is specially: if t ₁<T ₁, then illustrate that fault occurs in cable first half section, now the catadioptric situation of the transient state travelling wave of trouble spot on cable line as shown in Figure 5, obtains the time T that cable end piece second transient state travelling wave wave head arrives measurement point ₂, obtain the geographic distance L of trouble spot apart from cable head-end further _f, L _fcalculating formula is as follows:

$L_f=\frac{L(T_2-T_1)}{2(T_2-t_1)},$

Wherein, L is the geographical length of cable;

If t ₁>T ₁, then illustrate that fault occurs in the cable second half section, now the catadioptric situation of the transient state travelling wave of trouble spot on cable line as shown in Figure 6, obtains the time t that cable head-end second transient state travelling wave wave head arrives measurement point ₂, obtain the geographic distance L of trouble spot apart from cable head-end further _f, L _fcalculating formula is as follows:

$L_f=L-\frac{L(t_2-t_1)}{2(t_2-T_1)},$

Wherein, L is the geographical length of cable.

Described trouble spot is apart from the distance L of cable head-end _fcalculating formula derivation as follows: set the physical length of cable to be L as l, geographical length, suppose that relation is between the two approximately: l=λ L, λ are the scale-up factor between cable physical length l and geographical length L,

1., when fault occurs in cable first half section, transient state travelling wave velocity of wave is in the cable:

$\left\{\begin{array}{c}v=\frac{l}{T_2-t_1}\\ l=\mathrm{\&lambda;}L\end{array}\right.---\left(1\right)$

Trouble spot apart from the actual range of cable head-end is:

$\left\{\begin{array}{c}{l}_f=\frac{1}{2}v(T_2-T_1)\\ l_f=\mathrm{\&lambda;}{L}_f\end{array}\right.---\left(2\right)$

The geographic distance L of trouble spot apart from cable head-end is tried to achieve according to formula (1) and formula (2) _ffor:

$L_f=\frac{L(T_2-T_1)}{2(T_2-t_1)};$

2., when fault occurs in the cable second half section, transient state travelling wave velocity of wave is in the cable:

$\left\{\begin{array}{c}v=\frac{l}{t_2-T_1}\\ l=\mathrm{\&lambda;}L\end{array}\right.---\left(3\right)$

Trouble spot apart from the actual range of cable head-end is:

$\left\{\begin{array}{c}{l}_f=l-\frac{1}{2}v(t_2-t_1)\\ l_f=\mathrm{\&lambda;}{L}_f\end{array}\right.---\left(4\right)$

The geographic distance L of trouble spot apart from cable head-end is tried to achieve according to formula (3) and formula (4) _ffor:

$L_f=L-\frac{L(t_2-t_1)}{2(t_2-T_1)}.$

These computing method are not by the online Algorithms of Travelling Wave Based Fault Location of impact of cable velocity of wave change, and algorithm take into account the snake laying of cable, adopts this algorithm known conditions carried out needed for transient state travelling wave range finding to be only the geographical length of cable, convenience of calculation;

The calculating of 1 cable modulus current signal

Six conductor systems (as shown in Figure 2) that three-phase single-core power cables is made up of conductor wire core and protective metal shell, coupling is there is between this six conductor system, find range to adopt transient state travelling wave method in cable system, must independently modulus signal be become mutually to analyze by phase-model transformation matrix conversion the voltage of cable, current signal, adopt expansion Clark matrix to carry out phase-model transformation to cable system.Because outer modulus is with metal sheath layer with greatly for loop, propagation characteristic is unstable, and attenuation coefficient is large, and therefore we mainly study the transport property of modulus electric current in cable.Modulus current signal i ₁~ i ₆the calculating formula under expansion Clark matrixing as follows:

$\left\{\begin{array}{c}{i}_1=\frac{1}{\sqrt{3}}(i_a+i_b+i_c+i_A+i_B+i_C)\\ i_2=\frac{1}{\sqrt{6}}(i_a-2i_b+i_c+i_A-2i_B+i_C)\\ i_3=\frac{1}{\sqrt{2}}(i_a-i_c+i_A-i_C)\end{array}\right.\left\{\begin{array}{c}{i}_4=-\frac{1}{\sqrt{3}}(i_a+i_b+i_c)\\ i_5=-\frac{1}{\sqrt{6}}(i_a-2i_b+i_c)\\ i_6=-\frac{1}{\sqrt{2}}(i_a-i_c)\end{array}\right.$

Wherein, i _a, i _b, i _cbe respectively a phase core electric current, b phase core electric current, c phase core electric current, i _a, i _b, i _cbe respectively a phase sheath electric current, b phase sheath electric current, c phase sheath electric current, i ₁, i ₂, i ₃for outer modulus current signal, i ₄, i ₅, i ₆for interior modulus current signal.

The solution that in 2, modulus and outer modulus velocity of wave disturb

For cross interconnected cable, because the coordinated transposition of metal sheath layer connects, before and after POI, wave impedance is discontinuous.To the wave impedance matrix Z before POI ₁row, column carry out corresponding transposition can obtain POI after wave impedance matrix Z ₂, i.e. Z ₂=PZ ₁p ^t.For the transposition situation shown in Fig. 3, conversion bit matrix P is:

$P=\left[\begin{array}{cccccc}1& & & & & \\ & 1& & & & \\ & & 1& & & \\ & & & & & 1\\ & & & 1& & \\ & & & & 1& \end{array}\right]$

Wherein the putting in order as a phase core, b phase core, c phase core, a phase protective metal shell, b phase protective metal shell, c phase protective metal shell of impedance matrix.

By can be calculated the cable that certain 220kv tunnel lays, adopt the cross interconnected mode of Fig. 3, the wave impedance matrix when frequency is 1KHz is:

$Z_1=\left[\begin{array}{cccccc}39.84& 8.12& 6.71& 22.8& 8.13& 6.71\\ 8.12& 39.38& 8.12& 8.13& 22.33& 8.13\\ 6.71& 8.12& 39.84& 6.71& 8.13& 22.8\\ 22.8& 8.13& 6.71& 22.77& 8.14& 6.72\\ 8.13& 22.33& 8.13& 8.14& 22.3& 8.14\\ 6.71& 8.13& 22.8& 6.72& 8.14& 22.7\end{array}\right]$

Wave impedance matrix Z after POI ₂=PZ ₁p ^t, according to Z ₁, Z ₂the refraction coefficient matrix α of the capable ripple of current temporary state can be obtained _iwith reflection coefficient matrix β _i.The catadioptric relation of the capable ripple of current temporary state in modulus territory meets:

$\left\{\begin{array}{c}{i}_q=T_i{I}_{qm}\\ i_0=T_i{I}_{om}\\ i_q={\mathrm{\&alpha;}}_i{i}_0\end{array}\right.$

Wherein: I _omand I _qmbe respectively the incident modulus current matrix and refraction modulus current matrix that are made up of 6 modulus electric currents.Can be obtained fom the above equation: $i_{qm}=T_i^{-1}{\mathrm{\&alpha;}}_i{T}_i\&CenterDot;i_{om}.$

So the capable ripple of current temporary state at the refraction coefficient matrix in modulus territory is: be can be calculated by MATLAB:

${\mathrm{\&alpha;}}_{im}=\left[\begin{array}{cccccc}1.0001& -0.0560& -0.0302& 0.0001& -0.0564& -0.0457\\ -0.0092& 1.8107& 0.7298& -0.0117& 0.4234& 1.1992\\ -0.0059& -0.7132& 1.8949& -0.0055& -1.1612& 0.4894\\ -0.0000& 0.0270& 0.0156& 0.9999& 0.0271& 0.0232\\ 0.0012& -0.8385& -0.4833& 0.0020& 0.1614& -0.7183\\ 0.0040& 0.5015& -0.8670& 0.0045& 0.7262& 0.1332\end{array}\right]$

Pass before and after cross interconnected between modulus electric current is:

[I _qm1i _qm2i _qm3i _qm4i _qm5i _qm6] ^t=α _im[I _om1i _om2i _om3i _om4i _om5i _om6] ^t, α except diagonal entry _imthe element of the 4th row is very little, and is significantly less than other element respectively arranged, and illustrates that the component that modulus current signal 4 is transmitted in other modulus at cross interconnected point is minimum.By α _im44=0.9999, I _qm4=α _im44i _om4known incident modulus current signal 4 substantially all changes into refraction modulus current signal 4 at cross interconnected point, does not reflect.Therefore, adopt modulus current signal 4 as cross interconnected cable transient state travelling wave distance measuring signal, effectively can solve the complicated trouble spot reflection wave caused of transient state travelling wave catadioptric and be difficult to identification problem.

3 transient state travelling wave dispersions are on the impact of fault localization

Core and the metal sheath layer of high-tension cable have skin effect when being connected with alternating current, and the resistance of circuit and inductance can change with the change of power frequency.Circuit can present different transport propertys for the row ripple of different frequency component, and cable system at the propagation coefficient of frequency domain is:

$\mathrm{\&gamma;}\left(\mathrm{\&omega;}\right)=\sqrt{ZY}=\mathrm{\&alpha;}\left(\mathrm{\&omega;}\right)+j\mathrm{\&beta;}\left(\mathrm{\&omega;}\right)$

Wherein: [Z], [Y] are respectively impedance matrix and the admittance matrix of cable, α (ω) is amplitude attenuation coefficient, makes the amplitude attenuation of different frequency signals different; β (ω) is phase coefficient, and make the velocity of wave decay of different frequency signals different, the capable ripple of current temporary state and the capable ripple of voltage transient have identical propagation coefficient.

The transient state travelling wave produced during cable fault has continuous frequency spectrum from low to high, and because the transient state travelling wave velocity of propagation of different frequency component is different, decay is also different, and transient state travelling wave dispersion can occur along in cable line communication process.Transient state travelling wave wave head is tended towards stability, and overall velocity of wave is tending towards declining, and brings very large difficulty to the identification of wave head and the determination of velocity of wave in transient state travelling wave range finding.For the fault localization of overhead transmission line, Yan Shangke accepts the error produced by transient state travelling wave dispersion, and stronger for frequency dependent characteristic, and distance accuracy requires that higher cable line is but unacceptable.

For this reason, the application adopts the wavelet packet method as described in step (3) decompose and reconstruct transient state travelling wave,

4 by the location algorithm that transient state travelling wave velocity of wave affects

The application adopts the location algorithm as described in step (5), wherein, consider that in reality, cable generally adopts snake laying, the physical length of cable is also not easily tried to achieve, if the relation between the physical length l of cable and geographical length L is approximately: l=λ L, λ are the scale-up factor between snake laying cable physical length and geographical length.

Adopt said method, utilize electromagnetic transient simulation software ATP-EMTP to set up 220KV cable system realistic model (as shown in figure 11), the geographical length of cable is 4500m, and simulation step length is 1E-7s, simulation time is 0.01s, and the initial parameter of cable is as shown in table 1:

Table 1220KV single core cable initial parameter

Artificial mains network on-load normally runs, a phase core is there is to metal sheath layer short trouble in the t=0 moment, fault distance is set to 3000m, choose suitable time window, extract fault and the waveform of moment cable end at the whole story occurs as shown in Figure 7, wherein horizontal ordinate is time t/ms, and ordinate is electric current modulus signal amplitude I/KA.

3 layers of WAVELET PACKET DECOMPOSITION (being illustrated in figure 4 wavelet decomposition tree) are carried out to cable head-end and end waveform, fault transient travelling wave is resolved into the frequency band that 8 with identical frequency range are different, then according to the energy percentage of each frequency band of WAVELET PACKET DECOMPOSITION coefficient calculations of each frequency band as shown in Figure 8 and Figure 9.

By holding the whole story energy spectrum of fault traveling wave to know, the energy of row ripple mainly concentrates on frequency band 1 and frequency band 2, extracts the WAVELET PACKET DECOMPOSITION coefficient that cable holds row ripple frequency band 1 and frequency band 2 whole story respectively, and reconstruct fault transient travelling wave as shown in Figure 10.

Fault waveform is reconstructed to Figure 10 and carries out wavelet analysis, determine that initial row ripple arrives the time t of cable end at the whole story ₁, T ₁, according to t ₁, T ₁size failure judgement occur region.If fault occurs in cable first half section, then obtain the time T that cable end piece second wavefront arrives measurement point ₂, substitute into formula (1) and obtain fault distance.If failure judgement occurs in the cable second half section, obtain the time t that cable head-end second wavefront arrives measurement point ₂, substitute into formula (2) and obtain fault distance.

Claims (5)

1. the online fault distance-finding method of high-tension cable, is characterized in that, this fault distance-finding method comprises the following steps:

(1) signals collecting: gather transient state travelling wave current signal at cable end at the whole story;

(2) phase-model transformation: convert the current signal in step (1) to 6 mutual independently modulus current signal i by phase-model transformation ₁~ i ₆;

(3) decomposition and reconstruction of transient state travelling wave: the modulus current signal i in selecting step (2) ₄carry out WAVELET PACKET DECOMPOSITION, utilize WAVELET PACKET DECOMPOSITION coefficient to try to achieve the energy Ratios of each frequency band, then extract the frequency band of energy percentage >5%, reconstruct transient state travelling wave;

(4) wavelet analysis: carry out wavelet analysis to the transient state travelling wave after the reconstruct in step (3), determines that the capable ripple of initial transient arrives cable head-end time t ₁with the time T arriving cable end piece ₁;

(5) trouble spot calculates apart from the geographic distance of cable head-end: according to t in step (4) ₁, T ₁the region that occurs of size failure judgement, if fault occurs in cable first half section, then obtain the time T that cable end piece second transient state travelling wave wave head arrives measurement point ₂, and then obtain fault distance; If fault occurs in the cable second half section, then obtain the time t that cable head-end second transient state travelling wave wave head arrives measurement point ₂, and then obtain the geographic distance of trouble spot apart from cable head-end.

2. the online fault distance-finding method of a kind of high-tension cable according to claim 1, is characterized in that, modulus current signal i in described step (2) ₁~ i ₆calculating formula as follows:

$\begin{array}{cc}\left\{\begin{array}{c}{i}_1=\frac{1}{\sqrt{3}}(i_a+i_b+i_c+i_A+i_B+i_C)\\ i_2=\frac{1}{\sqrt{6}}(i_a-2i_b+i_c+i_A-2i_B+i_C)\\ i_3=\frac{1}{\sqrt{2}}(i_a-i_c+i_A-i_C)\end{array}\right.& \left\{\begin{array}{c}{i}_4=-\frac{1}{\sqrt{3}}(i_a+i_b+i_c)\\ i_5=-\frac{1}{\sqrt{6}}(i_a-2i_b+i_c)\\ i_6=-\frac{1}{\sqrt{2}}(i_a-i_c)\end{array}\right.\end{array}$

Wherein, i _a, i _b, i _cbe respectively a phase core electric current, b phase core electric current, c phase core electric current, i _a, i _b, i _cbe respectively a phase sheath electric current, b phase sheath electric current, c phase sheath electric current.

3. the online fault distance-finding method of a kind of high-tension cable according to claim 1, is characterized in that, described step (3) is specially:

(301) adopt wavelet packet analysis method by modulus current signal i ₄be decomposed into low-frequency approximation part and high frequency detail part, more described low-frequency approximation part is become second layer low frequency part and HFS with high frequency detail decomposed, decompose through i layer, modulus current signal i _4.just be decomposed 2 ⁱindividual different frequency band, utilizes the size of each frequency band energy of WAVELET PACKET DECOMPOSITION coefficient calculations, and the energy meter formula of each frequency band is as follows:

$E_{i,j}=\underset{k=1}{\overset{N}{\&Sigma;}}|d_{j,k}{|}^2$

Wherein, i is the number of plies of WAVELET PACKET DECOMPOSITION, and N is the sampling number of transient state travelling wave signal.D _j,k(j=0,1,2 ... 2 ⁱ-1, k=1,2 ... N) the WAVELET PACKET DECOMPOSITION coefficient of expression i-th layer, a jth node;

(302) energy of i-th layer of each frequency band is normalized, the number percent η shared by each frequency band energy can be obtained _j, its calculating formula is as follows:

${\mathrm{\&eta;}}_j=\frac{E_{i,j}}{\underset{j=0}{\overset{2^i-1}{\&Sigma;}}{E}_{i,j}}\&times;100\%$

(303) η is extracted _jthe frequency band of >5%, reconstruct transient state travelling wave.

4. the online fault distance-finding method of a kind of high-tension cable according to claim 1, is characterized in that, described step (5) is specially: if t ₁<T ₁, then illustrate that fault occurs in cable first half section, obtain the time T that cable end piece second transient state travelling wave wave head arrives measurement point ₂, obtain the geographic distance L of trouble spot apart from cable head-end further _f, L _fcalculating formula is as follows:

$L_f=\frac{L(T_2-T_1)}{2(T_2-t_1)},$

Wherein, L is the geographical length of cable;

If t ₁>T ₁, then illustrate that fault occurs in the cable second half section, obtain the time t that cable head-end second transient state travelling wave wave head arrives measurement point ₂, obtain the geographic distance L of trouble spot apart from cable head-end further _f, L _fcalculating formula is as follows:

$L_f=L-\frac{L(t_2-t_1)}{2(t_2-T_1)},$

Wherein, L is the geographical length of cable.

5. the online fault distance-finding method of a kind of high-tension cable according to claim 4, is characterized in that, described trouble spot is apart from the distance L of cable head-end _fconcrete computation process as follows: set the physical length of cable to be L as l, geographical length, suppose that relation is between the two approximately: l=λ L, λ are the scale-up factor between cable physical length l and geographical length L,

1., when fault occurs in cable first half section, transient state travelling wave velocity of wave is in the cable:

$\left\{\begin{array}{c}v=\frac{l}{T_2-t_1}\\ l=\mathrm{\&lambda;}L\end{array}\right.---\left(1\right)$

Trouble spot apart from the actual range of cable head-end is:

$\left\{\begin{array}{c}{l}_f=\frac{1}{2}v(T_2-T_1)\\ l_f={\mathrm{\&lambda;L}}_f\end{array}\right.---\left(2\right)$

The geographic distance L of trouble spot apart from cable head-end is tried to achieve according to formula (1) and formula (2) _ffor:

$L_f=\frac{L(T_2-T_1)}{2(T_2-t_1)};$

2., when fault occurs in the cable second half section, transient state travelling wave velocity of wave is in the cable:

$\left\{\begin{array}{c}v=\frac{1}{t_2-T_1}\\ l=\mathrm{\&lambda;}L\end{array}\right.---\left(3\right)$

Trouble spot apart from the actual range of cable head-end is:

$\left\{\begin{array}{c}{l}_f=1-\frac{1}{2}v(t_2-t_1)\\ l_f={\mathrm{\&lambda;L}}_f\end{array}\right.---\left(4\right)$

The geographic distance L of trouble spot apart from cable head-end is tried to achieve according to formula (3) and formula (4) _ffor:

$L_f=L-\frac{L(t_2-t_1)}{2(t_2-T_1)}.$